Answer:
the equation of the hyperbola is;(x²/81) - (y²/1600) = 1
Step-by-step explanation:
We are given that the hyperbola has;
Centre; 0,0
Vertex; 9,0
Focus; 41,0
Thus,the vertex and focus are on the x-axis. Thus, the equation for the hyperbola will have the form;
(x²/a²) - (y²/b²) = 1
Since The vertex is (9,0),so
a = 9 and a² = 9² = 81
Also,Since The focus is (41,0),so
c = 41 and c² = 41² = 1681
Solving for b², we have;
b² = c² - a²
b² = 1681 - 81
b² = 1600
b = √1600
b = 40
Thus,equation of hyperbola is;
(x²/9²) - (y²/40²) = 1
Which gives;
(x²/81) - (y²/1600) = 1
